Interim manager Roberto Di Matteo is a strong favourite to succeed Andre Villas-Boas, who was sacked in March, permanently having guided the Blues to FA Cup and Champions League glory this season.
However, it is still far from certain that the Italian will be handed the role on a full-time basis, having seen the club finish sixth in the Premier League.
And Gourlay has claimed that an appointment could be made sooner rather than later, with owner Roman Abramovich keen to have a new man in charge before the players report back to pre-season training in the first week of July.
When quizzed on when a new manager could be appointed, the Blues chief executive said: "Any time over the next couple of weeks and certainly by the time we go on tour.
"The players report back on July 4 or 5 and in an ideal world you want the coach in position by then."
Gourlay has hinted that Di Matteo is one of the candidates in the running for the position, acknowledging the success he has brought to the club could have a huge bearing on their choice.
"It certainly would have made the discussions a bit different," he added. "The fact that he has the Champions League on his CV helps him enormously.
"I know there has been speculation in the press and media about conversations with 'XYZ'. That has not been the case.
"We will sit down as a board of directors with our owner as quickly as we can and take our decision from there.
"We are going through that process now and then we'll sit down ... it's only been a couple of days [since the season ended]."
Russian oligarch Abramovich has seen nine managers come and go since purchasing the club in 2003, but Gourlay said the level of success speaks volumes regarding the trigger-happy billionaire.
"When you take into account how many managers have been sacked or not, when you look at the success we have had on the field it has been there," he said.
"We have demonstrated, whether you like our model or not, and we have delivered.
"Certainly since I have been in the role, we have always done what we believe is right for the football club in the long term."
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